Brendan Rodgers has told Luis Suárez he has threatened Liverpool's image and their prospects of receiving the benefit of doubt from referees with the admission he dived in an attempt to win a penalty against Stoke City.

The Liverpool manager issued his first public rebuke of the club's leading striker after Suárez revealed in an interview with Fox Sports Argentina that he cheated to try and win the game at Anfield in October. Following the goalless draw Tony Pulis, the Stoke manager, labelled Suárez "an embarrassment" and called on the Football Association to introduce retrospective action for diving, while Rodgers said he was at a loss to explain Suárez's actions but did not take the matter further.

Suárez's televised confession, however, has been deemed "unacceptable" by the Liverpool manager, who has said he would deal the Uruguay international "in house". Rodgers would not elaborate on the nature of any disciplinary action but it is understood Suárez will not be fined by Liverpool. The striker will not be censured by the FA for his comments.

"Certainly from our perspective it is unacceptable," said Rodgers. "It is not something we advocate here. Our ethics are correct. This is a big club and whatever people do say goes around the world, and what was said was wrong and not acceptable – he takes that and we move on. There is no one bigger than the club or the club's image. The comments, from our point of view as a club, are not what we would want to hear."

Suárez told Fox Sports Argentina that foreign players, particularly those from South America, are treated differently in the British media and that the reaction to his recent handball against Mansfield Town demonstrated unfair treatment. He also admitted: "Sometimes you do things on the field that later you think: 'Why the hell did I do that?' I was accused of falling inside the box in a match and it's true I did it that time, because we were drawing against Stoke at home and we needed anything to win it. But after that everybody jumped out to talk – the Stoke coach and the Everton coach – I understood that the name Suárez sells [papers]."

Rodgers has defended Suárez through several controversies but denied the striker's comments had undermined that support. He said: "I don't think I've been put in a difficult position. I've only ever called it honestly. I have defended him when I feel it is right and will continue to do that. I don't feel let down, I'll just call it like it is. I said at the time it was the wrong thing to do. I need to protect the club and the group and if anything puts that in jeopardy I will deal with that. Luis is aware of my feelings."

A key concern for the Liverpool manager is the potential impact of Suárez's admission on the team for the remainder of the season, with Rodgers fearing it could influence referees. He added: "It doesn't help him and, more importantly, it doesn't help the team. Anything detrimental to the team I don't take lightly. It's been difficult for us this season with regards penalties. We've only had one. The team always going into every game looking to win in the best possible way and sporting manner, and we don't want that to change.

"But this situation might affect people's thinking. I'm not saying it will do, but it could do. It might make people think twice about things and that's certainly something we don't want. The team puts maximum effort into the game and I wouldn't want second thoughts going into anybody's mind."

Unlike the Everton manager, David Moyes, who condemned Phil Neville immediately after he dived against Liverpool this season and revealed he had fined his captain a week's wages, Rodgers insisted the nature of Suárez's punishment should remain private.

He said: "I've spoken to Luis on it. I'm not sure it makes a big difference if we are saying he is fined one week's, two weeks' or four weeks' wages. The bottom line is that from my perspective as the manager and leader of the club it was wrong to say what he said. It was not acceptable. This club has always kept its matters in house, and that's what we will do."